Change zvose zvinobvira. zvinhu combinatorics

mudziyo munyika presupposes kuvapo hombe siyana zviitiko uye zvinhu. Panguva iyoyowo nesayenzi kunoratidza kuti hwaro ichi nezvakawanda ndiko kuva womumwe nhamba yenhengo. Unobva neimwe kuitira, zvinogumbura ndivo hwaro mapurani zvakagadzirwa zvenyika yakatipoteredza. Kudzidza uwandu zvose zvinobvira dzakasiyana ose ibatanidzo siyana zvinoriumba dzinobatanidzwa masvomhu, kunyanya chikamu yayo inonzi combinatorics.

Saka, sezvo zvinhu kudzidza discrete tsika kugamuchirwa, mumwe muzvizhinji (permutations, mubatanidzwa, kuchinjwa uye placement ose okunze) uye mafungiro pamusoro pavo (optionally kukwana hurongwa). combinatorics zvinhu vane pedyo chokuita geometry uye nemasvomhu, ivo akapotsa akava hwaro Masvomhu mune dzidziso mukana. Siyana minda siyana zivo zvisingaiti kufungidzira pasina kushandisa munda uyu nesayenzi. The rinofarirwa kupfuura davi masvomhu akatanga muna Statistical wefizikisi, genetics uye kombiyuta nesayenzi.

Uye mavambo rokuti ake, "combinatorial" zvinotora kubva 1666. In ake basa "Discourse pamusoro combinatorial nounyanzvi" yemasvomhu Leibniz nheyo nokuda pakuzadzisa bazi ichi wemasvomhu.

Kakawanda, kushandisa shoko rokuti "combinatorics", kufungisisa Chikamu discrete masvomhu, rinosanganisira zvikuru vakwanise Somuenzaniso, dzidziso calculators.

Zvinhu combinatorics rinowanzoshandiswa anounzwa muenzaniso combinatorial configurations. Accommodation, rearrangement, mubatanidzwa, akafanana uye partition nhamba huru zvinoriumba, izvo zvinowanikwa pachake zviga bazi ichi wemasvomhu.

Placement - ane akarayira yakatarwa imwe nhamba yenhengo enzvimbo yakatarwa, aine nhamba yakajeka pamusoro zvinhu. Permutation rinonzi zvachose akarayira yakatarwa munhu wakaiswa nhamba zvinhu. Combinatorics combine - kutaridza vatora uwandu zvinhu zvaisanganisira mune mashoko. Sets vari misiyano chete sezvakarayirwa okunze, asi ndivo chete chimiro, ichi ndicho musiyano pakati wemishonga uye placement. Kuwanda anofambidzana kunoenderana kukura yakatarwa uye uwandu zvinhu vanoumba yakatarwa, kubva inonwiwa achigadzirira akati combinatorial muenzaniso.

Tichitarisa pfungwa Zvinoumba, nokurikunda zvose somunhu cherudo mari akarayira kubva zvakanaka integers. Asi partition ose - ndiwo chero pfungwa sei ake disordered mubatanidzwa akanaka integers.

Zvinhu combinatorics zvinonzi nevakawanda kushandiswa muminda zivo siyana. Panguva iyoyo iye anoita chikamu ichi wemasvomhu nepaImba mukugumisa zvokuti kwaita vaunganidza mukwende mashoko ari mundima iyi kuti govera partitions.

Kufunga chirango chikamu chakanzi "Combinatorial enumeration" (quantifiable), kufungisisa kutapurirana kana Anoverenga zvichibvira configurations (somuenzaniso, permutations), izvo aumba kubva chinobatanidza finite seti. Zvinogoneka nokuiswa mitemo vamwe. Izvi zvinosanganisira Kusaoneka kana pachena okunze, kudzokorora chisarudzo zvakafanana okunze, uye zvichingodaro.

Kuti ngaaverenge nhamba configurations, uchishandisa dzenhoroondo nemitemo Kuwedzera uye chokuwanziridza. Zvinhu combinatorics muchikamu ichi chirango akashandiswa kugadzirisa-siyana mabasa akasiyana-siyana.

The STRUCTURAL combinatorics vakawedzera anoverengeka nyaya pamusoro girafu yokuti, inoratidza simba dzidziso matroids. Pakati zvikamu chirango chiri pachena combinatorics akanyanyisa, Ramsey dzidziso, fungidziro, topology, combinatorics infinitary.